Theory of Stochastic Integrals

Theory of Stochastic Integrals aims to provide an answer to the problem of phenomena that cannot be analyzed through the classical Itô theory by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales.

In applications of stochastic calculus, there are phenomena that cannot be analyzed through the classical Itô theory. It is necessary, therefore, to have a theory based on stochastic integration with respect to these situations.

Theory of Stochastic Integrals aims to provide the answer to this problem by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales, such as Volterra Gaussian processes, or processes with bounded p-variation among which we can mention fractional Brownian motion and Riemann-Liouville fractional process.

Features

• Self-contained treatment of the topic
• Suitable as a teaching or research tool for those interested in stochastic analysis and its applications

• Includes original results.

  Autorentext

Jorge A. León studied the PhD in equivalence of solutions to stochastic evolution equations at the Department of Mathematics of Cinvestav-IPN, Mexico. He has carried out joint research work with internationally recognized researchers. He has mainly contributed to the development of stochastic calculus and integration, and their applications to stochastic differential equations with different interpretations of stochastic integral. He has co-organized several conferences on stochastic analysis among which we can mention the Latin American Congress of Probability and Mathematical Statistics (CLAPEM), the joint meeting between USA and Mexico, Bernoulli-IMSWorld Congress, Symposium on Probability and Mathematics Statistics, which was the most important meeting in probability at Mexico, etc. He has taught at Cinvestav-IPN for 35 years.

Klappentext

Theory of Stochastic Integrals aims to provide an answer to the problem of phenomena that cannot be analyzed through the classical Itô theory by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales.

Inhalt

1. Basic Tool and Concepts. 2. Riemann-Stieltjes integral. 3. Classical Stochastic Integration. 4. Divergence Operator. 5. Forward Integration. 6. Stratonovich Integration. 7. Stochastic Differential Equations. 8. Appendix.